"Explain the notion of freedom without the presence of authority."
I can help you on this one. There is authority which is needed, and then there is abuse of authority which is not needed. To take away the right of a law abiding citizen to self defend is an abuse of authority.
But autority needs to be present in order to secure freedom...is that not right?
It seems that you agreed to take someone's ability to self defend based on your own willingness to exercise authority over others.
You have no problem with setting up laws under which all must live (whether they all like it or not), then you also have no problem with taking away the rights of self defense of those who don't live under the laws you've enacted, against their will.
"Freedom is about the willingness of every single human being to cede to lawful authority a great deal of discretion about what you do."
The statement I quoted from you is in complete agreement with what Rudy said.